SYDNEY, Feb 28 (Reuters) - Virgin Australia Holdings Ltd , Australia's second biggest airline, scrapped plans to potentially go private on Wednesday, sparking concerns that a major Chinese shareholder, HNA Tourism, may be about to exit, and leading to a sharp fall in its share price.

The surprise decision overshadowed the airline's best underlying half-yearly profit in a decade. Small shareholders have stuck with their investments in hopes the company would make good on plans to buy them out at a premium.

Just 10 percent of Virgin's stock is openly traded on the share market but analysts watch its register carefully since it includes Richard Branson, with 10 percent, and Singapore Airlines Ltd, Etihad Airways and China's Nanshan Capital Holdings Ltd and HNA Tourism Group Co Ltd , which each hold about 20 percent.

HNA, part of an aviation-to-services conglomerate, has been selling assets to alleviate severe financial strain after a $50 billion acquisition spree over two years sparked scrutiny of its opaque ownership and use of leverage.

"Following discussions with the major shareholders the board has decided not to privatise the company," Chairwoman Elizabeth Bryan said in a statement on Wednesday.

Bryan did not give a reason for the company's decision to reverse a move it flagged in 2017.

Asked about the decision on an analyst call, Virgin CEO John Borghetti said he was "here to run the company and we're doing the best we can".

"It's the decision and we move on," he added.

Virgin shares were down 6 percent at 24.5 Australian cents by mid-session, close to the record lows the stock has traded at after years of losses and rising debt forced it to sell more shares. The broader market was down 0.4 percent.

The company meanwhile posted a 142 percent jump in first-half underlying profit and swung to an interim net profit for the first time in two years as more Australians chose to fly and fewer seats enabled it to charge higher fares.

The airline added that it expected an improvement in underlying performance in the second half of fiscal 2018.

Underlying profit was A$102.5 million ($79.80 million) for the six months ended Dec. 31, from A$42.3 million the previous year. Net profit of A$4.4 million compared with a A$21.5 million loss a year earlier.

Last week, Virgin's larger rival and Australian flagship carrier Qantas beat market expectations with a record first-half profit, also largely because of fare hikes and higher demand at its domestic unit.

HNA, which bought into Virgin in May 2016, was not immediately available for comment

($1 = 1.2845 Australian dollars) (Reporting by Byron Kaye in SYDNEY and Rushil Dutta in BENGALURU Editing by Simon Cameron-Moore)